Exam MAS-I Practice Question 100
Study guide: Exam MAS-I
An auto insurer has two accident years of data, split by vehicle age:
| Accident year | Vehicle age | Exposure | Claims |
|---|---|---|---|
| 2023 | New | 2,000 | 100 |
| 2023 | Old | 8,000 | 440 |
| 2025 | New | 8,000 | 500 |
| 2025 | Old | 2,400 | 165 |
Two Poisson GLMs with a log link and an offset of \ln(\text{exposure}) are fitted, each with New as the base level:
- Model 1: vehicle age is the only predictor.
- Model 2: vehicle age and accident year (categorical) are both predictors, with no interaction.
Part a (1 point)
Calculate the Old/New frequency relativity fitted by Model 1. Give your answer to three decimal places.
Part b (1 point)
Calculate the Old/New frequency relativity fitted by Model 2. Give your answer to three decimal places.
Part c (1 point)
Which relativity should the rating plan use for old vehicles, and why?
- A) 0.970, because accident year is not a rating variable and so should not be in the model
- B) 1.100, because accident year absorbs the trend that the mix shift had loaded onto vehicle age
- C) 0.970, because Model 1 has fewer parameters and is therefore preferred by parsimony
- D) 1.035, the average of the two, since each model captures part of the true effect
- E) 1.375, the product of 1.100 and the 2025 accident-year relativity of 1.25
Answer this question and see the worked solution